"Andrew doesn't believe in regret"
This line is so foundational to Andrew's character! I always see folk talk as if Andrew is neurologically incapable of regret, as if he cannot actually feel the emotion of regret. I think that Andrew can, and perhaps does, feel regret in canon. What the "Andrew doesn't believe in regret" line actually shows is that Andrew works hard to only make decisions that he can stand by - including his decision to be with Neil.
The idea that Andrew doesn't do regret comes up twice - and both times it's used to reassure Neil that Andrew wants him!
Renee says it first, after explaining how she and Andrew split protection of the Foxes:
At this point, andreil is well under way. Neil knows that Andrew likes him, and Neil is falling HARD for Andrew (This conversation w/ Renee happens immediately after the rooftop "90% / I want to see you lose control" conversation). In this context, telling Neil that Andrew doesn't believe in regret tells Neil that Andrew doesn't regret keeping him, that Andrew doesn't regret any of it: not the power that he's handed Neil, not Neil's interfering with his and Aaron's relationship, not any feelings that might be developing between them. It reaffirms Neil's vision of Andrew as strong, in control, a pillar that Neil can lean on without breaking - all the things that make Neil fall in love with Andrew.
The second mention of Andrew not doing regret is during Andrew and Neil's first kiss:
Here, Neil really wants to kiss Andrew! He is trying to reassure himself that it's ok to keep kissing him, given that Neil is convinced that he's going to die soon. This is the day that Neil calls Andrew for help mid panic attack, and the day that he buys Andrew the Maserati. Neil is fully aware that Andrew is important to him and already committed to not hurting him. So he takes Renee's words and uses them to reassure himself that Andrew IS strong enough and willing enough to take the consequences of his decisions, even if those consequences mean letting Neil in for this little bit of intimacy before Neil's inevitable death.
Funnily enough, when Neil is NOT trying to reassure himself that Andrew doesn't regret Neil himself, this is Neil's assessment of Andrew's capacity for regret:
Neil clearly disapproves of the Upperclassmen's attitude to Andrew. A missplaced sense of necessity - in other words, Neil thinks that Andrew is capable of regretting his actions and of understanding other people's anger. The Upperclassmen are wrong to think that Andrew is just wired to not feel emotion (wrong to think he's a "sociopath"). When really, Andrew does not regret his actions simply because he thinks that they were correct. [And this scene comes in between the 2 examples above, so we're not seeing Neil change his mind - we're literally seeing him clinging to the idea that Andrew doesn't regret when it comes to NEIL specifically!]
As for Andrew himself, he says the word "regret" only once in canon.... and it's when he agrees to go to the Hemmicks' for dinner. He tells Neil that: "we're all going to regret this". Which I mean, ouch. But also the line is "we" , which very clearly includes Andrew himself in the group of people who he expects to feel regret.
Tellingly, Neil's response to "we're all going to regret this" is to ask if Andrew really killed Tilda, and Andrew makes it clear that (a) he did kill her and (b) he doesn't regret it. I think it's interesting that the text is placed this way - as if to point out that Andrew's lack of remorse over Tilda is not because of his neurological wiring or even his trauma, but because his fully considered take on the situation is still that he did the right thing. Unlike going to the Hemmicks', which he doesn't think is the correct thing to do, and so is something he expects to regret.
This desire to keep a tight lid on his emotions by strictly controlling situations is completely in character for Andrew (and he doesn't just do it with regret! Fear too: "what were you doing on the roof?" "Feeling"). It's also in character to want complete control over his own actions - Andrew over-analyses and seeks to control every aspect of a situation so that his own actions are completely under his control, are exactly what HE wants to do (which is also why the medication is so very terrible for him!). Andrew doesn't believe in regret not because he doesn't feel the emotion, but because he is extremely CAREFUL to make choices that he will not regret. Regret is pointless (like guilt or shame) in the sense that if you have analysed the situation, set your mind on the outcome you want & acted accordingly, then what is there to be regret?
To be clear, I don't deny that Andrew experiences less emotion in general than is typical. We know that Andrew experiences numbness, and that he cares about very few things. Nora says in the EC that even post-canon he doesn't sulk or get grumpy, he's way more likely to just shut down entirely instead. @andrewminyard-josten says in this post that Andrew's apathy is both natural to him and a controlled self-defence mechanism - and I essentially agree with this. Andrew may experience less emotion because his neurology/trauma makes him prone to numbness - but at the same time he goes to efforts to manage and control the emotions that he DOES experience. Crucially, the full range of emotions are available to Andrew. He might feel them in a more muted way, or he might sometimes shut down rather than feel them - but avoiding an emotion like regret all together (not "believing" in regret) comes from his actions.
I think this matters because if we move away from thinking that Andrew just can't experience regret, then it means that Andrew fully endorses all of his canon behaviour! All of the things that he does not regret - killing Tilda, drugging Neil, choking Allison, strangling Kevin, loving Neil - are things that he doesn't regret not because he is incapable of feeling the emotion, but because he completely and whole heartedly stands by them. He would do it all again, if given the chance. Good for him, I say.